David Sumpter
BLOOMSBURY PRESS 2016, 304 pages
PRICE (HARDBACK) £16.99 ISBN 978-1-4729-2412-4
This is a well-written and enjoyable book which will appeal to readers of Mathematics Today who follow football. The author is a Professor of Mathematics who, in his professional life, works to apply maths to other fields and, in his personal life, is a passionate follower of football. His stated aim in writing this book is not to ‘reduce the whole of the beautiful game to mathematics and science’, but to show that ‘football and maths can work together to create powerful analogies’ and present ‘a more accessible and creative style of mathematics’.
And this book is certainly brimming with analogies and interesting examples. For example the methods used to map the romantic and sexual network of an American High School are used to produce a passing network for the England football team.
The style of this book is very descriptive, and its 300 pages are replete with clear and helpful diagrams. The few equations presented are relatively simple, and there is little football jargon. The author states in his introduction that he assumes no in depth knowledge of either mathematics or football, and certainly a reader with some A-level Statistics and a passable knowledge of football over the last ten years will be able to read this book with ease. That said, there are twenty pages of notes at the end of this book, for those readers who want to look into the more technical details of the ideas presented.
So to the content of this book, which is divided into three parts. Part I examines events on the pitch. Chapter 1 begins by showing that the average number of goals scored in a match follows a Poisson distribution. The author then considers whether historical final league positions combined with random simulations can be used to predict future final league positions.
In Chapter 2 team formations are illustrated using minimum spanning trees. Networks of slime moulds are discussed, and then the team formation of Guardiola’s Barcelona is analysed to identify just why it was so successful.
Chapter 3 considers the position and movement of players, with flow field diagrams used to model the interactions of attackers and defenders. The chapter ends with one of the highlights of the book, using flow fields and heat maps to compare the playing styles of Pirlo and Schweinsteiger.
The title of Chapter 4, Statistical Brilliance, refers to Messi and Ronaldo who, in recent years have rewritten records for goals scored in a season. Extreme-value distributions are discussed in this context and others.
Chapter 5 is a brief look at how Newton’s Laws of Motion can be used to model Zlatan’s bicycle kick against England. Yes, that bicycle kick.
Part II looks at team management. In 1981 the number of points for a win increased from two to three, and Chapter 6 uses expected values to model the theoretical impact of this change on a team’s incentives to attack and defend. The author illustrates some of the finer points of this chapter by making analogies with the hierarchical interactions between shore crabs.
Chapter 7 uses networks to illustrate the passing characteristics of different teams. These illustrations are then used, for example, to explain the results of matches between England, Italy and Spain at Euro 2012.
Chapter 8 considers the value of teamwork. The methods of Lobanovskyi, the legendary former manager of Dynamo Kiev and the USSR, are discussed. The author then looks at how a successful team will be more than the sum of its parts, and he also considers the value of a charismatic leader.
Chapter 9 considers teamwork and the synchronisation of movement in groups. The author describes models for swarms of locusts, and explains that models of animal behaviour are now being applied to team performance. The field of collective soccer analytics is briefly mentioned, with an acknowledgement that data on player movement is not readily available.
Part III is focused on the supporters. Chapter 10 looks at the behaviour of crowds, with an eye on stadium design and crowd safety. Theories relating to the spread of chanting or applause are described, with a discussion of S-shaped curves, social contagion and social recovery.
Chapter 11 explains how bookmakers set the spread for spread betting, and asks whether an individual can beat the spread. In Chapter 12 the author devises his own strategies for beating the bookmakers, and then in Chapter 13 tests these strategies and analyses his success (or otherwise).
I thoroughly enjoyed this book and cannot recommend it highly enough.
Narinder Singh Basra AMIMA
Book review published in Mathematics Today April 2017
